In practical management of an entire water distribution system, it is very important to define optimal renewal time for pipelines. Reasons mainly include their deterioration, invisibility as an underground system and the adverse impact on society in the case of leakage. Thus, this paper proposes a mathematical model to satisfy this actual need. The model is developed based on Weibull hazard function and least life-cycle cost estimation approach. This model enables us to determine not only the deterioration rate of pipelines but also optimal renewal time. Attention is further focused on finding optimal pipeline materials. Empirical study was conducted on the dataset of a pipeline system in the city of Osaka, Japan.